Valeri P. Maltsev

The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength

In this paper we investigate the capabilities of the discrete dipole approximation (DDA) to simulate scattering from particles that are much larger than the wavelength of the incident light, and describe an optimized publicly available DDA computer program that processes the large number of dipoles required for such simulations. Numerical simulations of light scattering by spheres with size parameters x up to 160 and 40 for refractive index m ¼ 1:05 and 2, respectively, are presented and compared with exact results of the Mie theory. Errors of both integral and angle-resolved scattering quantities generally increase with m and show no systematic dependence on x: Computational times increase steeply with both x and m, reaching values of more than 2 weeks on a cluster of 64 processors. The main distinctive feature of the computer program is the ability to parallelize a single DDA simulation over a cluster of computers, which allows it to simulate light scattering by very large particles, like the ones that are considered in this paper. Current limitations and possible ways for improvement are discussed. r 2007 Elsevier Ltd. All rights reserved.

Experimental and theoretical study of light scattering by individual mature red blood cells by use of scanning flow cytometry and a discrete dipole approximation

Elastic light scattering by mature red blood cells (RBCs) was theoretically and experimentally analyzed by use of the discrete dipole approximation (DDA) and scanning flow cytometry (SFC), respectively. SFC permits measurement of the angular dependence of the light-scattering intensity (indicatrix) of single particles. A mature RBC is modeled as a biconcave disk in DDA simulations of light scattering. We have studied the effect of RBC orientation related to the direction of the light incident upon the indicatrix. Numerical calculations of indicatrices for several axis ratios and volumes of RBC have been carried out. Comparison of the simulated indicatrices and indicatrices measured by SFC showed good agreement, validating the biconcave disk model for a mature RBC. We simulated the light-scattering output signals from the SFC with the DDA for RBCs modeled as a disk-sphere and as an oblate spheroid. The biconcave disk, the disk-sphere, and the oblate spheroid models have been compared for two orientations, i.e., face-on and rim-on incidence, relative to the direction of the incident beam. Only the oblate spheroid model for rim-on incidence gives results similar to those of the rigorous biconcave disk model.

Light-scattering properties of individual erythrocytes

We have studied the light-scattering properties of human erythrocytes both experimentally and theoretically. In the experimental study measurements were performed with a Scanning Flow Cytometer (SFC). The SFC can measure the light-scattering pattern (indicatrix) of an individual particle over an angular range of 10-60 degrees. We have observed polymorphism in the measured set of indicatrices. To understand the reason for this polymorphism, we have made a theoretical study of the scattering properties of erythrocytes. The Wentzel-Kramer-Brillouin approximation has been employed to calculate indicatrices of individual erythrocytes in different orientations relative to the incident light beam. The indicatrices were calculated over an angular range of 15-35 degrees. A comparison of the experimentally measured and theoretically calculated indicatrices shows that the polymorphism is due mainly to the different orientation of the erythrocytes in the flow. The effect caused by the Poiseuille profile of the flow on an individual erythrocyte within the SFC cuvette capillary was studied theoretically by use of the Stokes approximation. Rotation of an erythrocyte was predicted by this theoretical analysis, and this prediction was further verified by comparison with experimental results.

Broadening of Operating Frequency Band of Magnetic-Type Radio Absorbers by FSS Incorporation

Problems of the theory of radio absorbers (RAs) involving frequency selective surfaces (FSSs) are considered. A design procedure for these RAs is described that takes into account the multiparameter character of the problem and allows one to determine the optimal characteristics of an FSS that provide the maximal operating bandwidth. RAs for a range of 1-17 GHz are obtained on the basis of polymer composites filled with carbonyl iron and Co2Z ferrite, into which an FSS in the form of a biperiodic array of thin metal rings is embedded. It is shown that the application of such an FSS allows one to increase the operating frequency bandwidth of a magnetic-type RA by a factor of more than 1.5 virtually almost without increasing the thickness of the absorber. Substantially, several types of FSS-based layered magnetodielectric RAs have been produced by compressing molding technique, including a 3-mm-thick RA with an operating bandwidth of 1.05-2.7 GHz, a 2-mm-thick RA with an operating bandwidth of 1.7-4.4 GHz, and a 1.6-mm-thick RA with an operating bandwidth of 6.7-16.1 GHz.

Individual Escherichia coli Cells Studied from Light Scattering with the Scanning Flow Cytometer

BACKGROUND Flow cytometry is a powerful tool for the analysis of individual particles in a flow. Differential light scattering (an indicatrix) was used for many years to obtain morphologic information about microorganisms. The indicatrices play the same role for individual particle recognition as a spectrum for substance characterization. We combined two techniques to analyze the indicatrix of the cells for the purpose of developing a database of light-scattering functions of cells. METHODS The scanning flow cytometer (SFC) allows the measurement of the entire indicatrix of individual particles at polar angles ranging from 5 degrees to 100 degrees. In this work, light-scattering properties of Escherichia coli have been studied both experimentally and theoretically with the SFC and the T-matrix method, respectively. The T-matrix method was used because of the nonspherical shape of E. coli cells, which were modeled by a prolate spheroid. RESULTS The indicatrices of E. coli cells were stimulated with T-matrix method at polar angles ranging from 10 degrees to 60 degrees. The absolute cross-section of light scattering of E. coli has been determined comparing the cross section of polystyrene particles modeled by a homogeneous sphere. The E. coli indicatrices were compared for logarithmic and stationary phases of cell growth. CONCLUSIONS The indicatrices of E. coli were reproducible and could be used for identification of these cells in biologic suspensions. The angular location of the indicatrix minimum can be used in separation of cells in logarithmic and stationary phases. To use effectively the indicatrices for that purpose, the light-scattering properties of other microorganisms have to be studied.

Single-particle sizing from light scattering by spectral decomposition

A Fourier transform was applied to size an individual spherical particle from an angular light-scattering pattern. The position of the peak in the amplitude spectrum has a strong correlation with the particle size. A linear equation retrieved from regression analysis of theoretically simulated patterns provides a relation between the particle size and the location of the amplitude spectrums peak. The equation can be successfully applied to characterize particles of size parameters that range from 8 to 180 (corresponding to particle sizes that range from 1.2 to 27.2 microm at a wavelength of 0.633 microm). The precision of particle sizing depends on the refractive index and reaches a value of 60 nm within refractive-index region from 1.35 to 1.70. We have analyzed four samples of polystyrene microspheres with mean diameters of 1.9, 2.6, 3.0, and 4.2 microm and a sample of isovolumetrically sphered erythrocytes with a scanning flow cytometer to compare the accuracy of our new method with that of others.

Calibration-free method to determine the size and hemoglobin concentration of individual red blood cells from light scattering

At present, hemoglobin concentration and the volume of an erythrocyte can be determined from the intensities of light scattered by an individual cell at fixed angular intervals. This method is used in modern hemoglobin analyzers, but it requires calibration of optical and electronic units by certified particles of known size and refractive index. We describe a method that is based on the parametric solution of an inverse light-scattering problem and does not require a calibration procedure. The method is based on the use of parameters of the entire angular light-scattering pattern, called an indicatrix here. These parameters do not depend on the absolute intensity of light scattering. The indicatrix parameters form approximating equations that relate these parameters to the size and the phase-shift parameters of the particle. The applicability of the method is demonstrated by measurement of the indicatrices of individual sphered erythrocytes. The indicatrices of the individual erythrocytes were measured with a scanning flow cytometer at an angular range of from 15 to 55 deg. The volume and the hemoglobin concentration have been calculated by use of the developed method and by fitting of the experimental indicatrices to the indicatrices calculated from the Mie theory.

Accurate measurement of volume and shape of resting and activated blood platelets from light scattering

Abstract. We introduce a novel approach for determination of volume and shape of individual blood platelets modeled as an oblate spheroid from angle-resolved light scattering with flow-cytometric technique. The light-scattering profiles (LSPs) of individual platelets were measured with the scanning flow cytometer and the platelet characteristics were determined from the solution of the inverse light-scattering problem using the precomputed database of theoretical LSPs. We revealed a phenomenon of parameter compensation, which is partly explained in the framework of anomalous diffraction approximation. To overcome this problem, additional a priori information on the platelet refractive index was used. It allowed us to determine the size of each platelet with subdiffraction precision and independent of the particular value of the platelet aspect ratio. The shape (spheroidal aspect ratio) distributions of platelets showed substantial differences between native and activated by 10 μM adenosine diphosphate samples. We expect that the new approach may find use in hematological analyzers for accurate measurement of platelet volume distribution and for determination of the platelet activation efficiency.

Light-scattering flow cytometry for identification and characterization of blood microparticles

We describe a novel approach to study blood microparticles using the scanning flow cytometer, which measures light scattering patterns (LSPs) of individual particles. Starting from platelet-rich plasma, we separated spherical microparticles from non-spherical plasma constituents, such as platelets and cell debris, based on similarity of their LSP to that of sphere. This provides a label-free method for identification (detection) of microparticles, including those larger than 1 μm. Next, we rigorously characterized each measured particle, determining its size and refractive index including errors of these estimates. Finally, we employed a deconvolution algorithm to determine size and refractive index distributions of the whole population of microparticles, accounting for largely different reliability of individual measurements. Developed methods were tested on a blood sample of a healthy donor, resulting in good agreement with literature data. The only limitation of this approach is size detection limit, which is currently about 0.5 μm due to used laser wavelength of 0.66 μm.

Determination of volume, shape and refractive index of individual blood platelets

Light scattering patterns (LSP) of blood platelets were theoretically and experimentally analyzed. We used spicular spheroids as a model for the platelets with pseudopodia. The discrete dipole approximation was employed to simulate light scattering from an individual spicular spheroid constructed from a homogeneous oblate spheroid and 14 rectilinear parallelepipeds rising from the cell centre. These parallelepipeds have a weak effect on the LSP over the measured angular range. Therefore, a homogeneous oblate spheroid was taken as a simplified optical model for platelets. Using the T-matrix method, we computed the LSP over a range of volumes, aspect ratios and refractive indices. Measured LSPs of individual platelets were compared one by one with the theoretical set and the best fit was taken to characterize the measured platelets, resulting in distributions of volume, aspect ratio and refractive index.